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Systems Optimization Laboratory

Stanford University
Dept of Management Science and Engineering (MS&E)

Huang Engineering Center

Stanford, CA 94305-4121  USA

covLSQR: Sparse Equations and Least Squares

  • AUTHORS: Ekaterina Kostina, Michael Saunders, Inga Schierle.
  • CONTRIBUTORS: Chris Paige.
  • CONTENTS: Implementation of a conjugate-gradient type method for solving sparse linear equations and sparse least-squares problems:  Solve
    Ax = b
    minimize || Ax - b ||2
    minimize || Ax - b ||2 + d2 ||x||2
    the same as LSQR.
    Special feature: LSQR and covLSQR can estimate the diagonal of C = (A'A + d2 I) -1. covLSQR can also estimate any principal submatrix of C. It was developed to estimate the parameter covariance matrix for large parameter estimation problems with nonlinear equality constraints, as described in Technical Report SOL 2009-1 (see below).
    E. Kostina, M. A. Saunders, and I. Schierle, Computation of covariance matrices for constrained parameter estimation problems using LSQR, Report SOL 2009-1, 11 pages.
    14 Jun 2009: Technical report.
    24 Dec 2010: Matlab files.

  • Matlab files
    Contributed 24 Dec 2010 by Michael Saunders ( and Inga Schierle (